Let's go through each problem step by step and solve them.

1. $50 - 6 + 15 \div 5$

• Division first: $15 \div 5 = 3$
• Now the expression is: $50 - 6 + 3$
• Subtract: $50 - 6 = 44$
• Add: $44 + 3 = 47$

Answer: $47$

2. $\frac{4}{3} - \frac{1}{2}$

• Find the least common denominator (LCD) of 3 and 2, which is 6.
• Convert fractions:
  • $\frac{4}{3} = \frac{8}{6}$
  • $\frac{1}{2} = \frac{3}{6}$
• Subtract:
  • $\frac{8}{6} - \frac{3}{6} = \frac{5}{6}$

Answer: $\frac{5}{6}$

3. $4 \frac{2}{5} + 3 \frac{1}{2}$

• Convert to improper fractions:
  • $4 \frac{2}{5} = \frac{22}{5}$
  • $3 \frac{1}{2} = \frac{7}{2}$
• Find the LCD of 5 and 2, which is 10.
• Convert fractions:
  • $\frac{22}{5} = \frac{44}{10}$
  • $\frac{7}{2} = \frac{35}{10}$
• Add:
  • $\frac{44}{10} + \frac{35}{10} = \frac{79}{10}$
• Convert back to a mixed number:
  • $\frac{79}{10} = 7 \frac{9}{10}$

Answer: $7 \frac{9}{10}$

4. $\frac{2}{3} \times 4 \frac{1}{10}$

• Convert to improper fractions:
  • $4 \frac{1}{10} = \frac{41}{10}$
• Multiply:
  • $\frac{2}{3} \times \frac{41}{10} = \frac{82}{30}$
• Simplify:
  • $\frac{82}{30} = \frac{41}{15}$ (since 82 and 30 have a GCD of 2)
• Convert to a mixed number:
  • $\frac{41}{15} = 2 \frac{11}{15}$

Answer: $2 \frac{11}{15}$

5. $-\frac{1}{2} \div \frac{5}{4}$

• Division by a fraction means multiplying by the reciprocal:
  • $-\frac{1}{2} \times \frac{4}{5}$
• Multiply:
  • $\frac{-1 \times 4}{2 \times 5} = \frac{-4}{10}$
• Simplify:
  • $\frac{-4}{10} = \frac{-2}{5}$

Answer: $-\frac{2}{5}$

Do you want more details on any step? Let me know!

Related Questions:

1. How do you determine the least common denominator (LCD) of two fractions?
2. What are the steps to convert a mixed number to an improper fraction?
3. How do you simplify fractions after multiplication?
4. What is the rule for dividing fractions?
5. How can you check if your answer is correct when working with fractions?

Tip:

When dealing with fractions, always look for ways to simplify before performing operations to make calculations easier!